Probability and Statistics
This page contains resources about Probability Theory and Statistics in general. More specific information is included in each subfield. Subfields and Concepts See Category:Probability and Statistics for all its subfields. * Statistical Inference / Inferential Statistics ** Frequentist Inference *** Hypothesis Testing *** Confidence Intervals ** Bayesian Inference *** Bayes Factor *** Credible Intervals *** Variational Inference *** Bayesian Nonparametrics *** Empirical Bayes Method / Maximum Marginal Likelihood ** Inductive inference ** Causal Inference ** Interval Estimation ** Estimation Theory / Point Estimation *** Least Squares filters *** Monte Carlo Methods *** Expectation-Maximization Algorithm *** Regularization *** Maximum Likelihood Method *** Bayes Estimator **** Bayesian Decision Theory ** Decision Theory *** The Expected Loss Principle *** Optimal decision rules *** Bayesian Decision Theory / Bayesian Estimator *** Cost function / Loss function *** Risk function *** Admissibility *** Unbiasedness *** Minimaxity ** Analysis of Variance (ANOVA) ** Multivariate Analysis of Variance (MANOVA) ** Analysis of Covariance (ANCOVA) ** Algorithmic Information Theory *** Minimum Description Length (MDL) *** Minimum Message Length (MML) *** Occam's Razor *** Kolmogorov Complexity ** Model Selection and Evaluation *** Akaike Information Criterion (AIC) *** Bayesian Information Criterion (BIC) *** Deviance Information Criterion (DIC) *** Bayesian Predictive Information Criterion (BPIC) *** Focused Information Criterion (FIC) *** Bayesian Model Selection / Bayesian Model Comparison **** Bayesian Model Averaging *** Bayesian Parameter Estimation **** Bayesian Nonparametrics *** Minimum Description Length (MDL) *** Minimum Message Length (MML) *** Akaike Final Prediction Error (FPE) *** Parzen's Criterion Autoregressive Transfer Function (CAT) *** Cross-Validation *** Statistical hypothesis testing (for Multilevel Models / Nested Models only) **** Lagrange multiplier test / Score test / Score Method **** Likelihood-ratio test **** Wald test * Statistical Models ** Regression Analysis *** Parametric Regression *** Nonparametric Regression ** Generalized Linear Model (GLM or GLIM) *** Ridge regression / Tikhonov regularization *** Least absolute shrinkage and selection operator (LASSO) *** Elastic Nets *** RANSAC *** Logistic Regression ** Probabilistic Models *** Stochastic Models (Stochastic Processes, Random Fields, ...) *** Probabilistic Graphical Models *** Latent Variable Models (i.e. Partially Observed Probabilistic Models) **** Continuous Latent Variable Models **** Discrete Latent Variable Models ** Time Series Models *** ARMA Models *** Volatility Models / Conditional Heteroscedastic Models / ARCH Models *** ARMA Metrics (e.g. Martin Distance) ** Linear Dynamical Systems / State Space Models *** State-Space Models with Regime Switching / Jump Markov Linear Systems / Switching LDS ** Mixed Models (not to be confused with Mixture Models) *** Best linear unbiased prediction (BLUP) * Probability Theory ** Random Variables *** Continuous Random Variables **** Probability Density Function *** Discrete Random Variables **** Probability Mass Function *** Jointly Distributed Random Variables **** Joint Density Function *** Independent Random Variables *** Uncorrelated Random Variables ** Moments of a distribution *** First Moment / Mean *** Second Moment / Variance *** Third Moment / Skewness *** Fourth Moment / CKurtosis ** Probabilistic Models ** Stochastic Convergence ** Probability Space ** Measure Space ** State Space ** Theorem of Total Probability ** Central Limit Theorem ** Martingale Theory ** Ergodic Theory ** Decision Theory ** Measure Theory ** Utility Theory Online Courses Video Lectures *Probabilistic Systems Analysis and Applied Probability by John Tsitsiklis *Introduction to Probability - The Science of Uncertainty by edX - very similar to the above *Probability by Salman Khan *Statistics by Salman Khan Lecture Notes *Introduction to Probability and Statistics by Dmitry Panchenko Books * Gentle, J. E. (2013). Theory of statistics. * Abu-Mostafa, Y. S., Magdon-Ismail, M., & Lin, H. T. (2012). Learning From Data. AMLBook. * Diez, D. M., Barr, C. D., & Cetinkaya-Rundel, M. (2012). OpenIntro Statistics. CreateSpace. * Lavine, M. (2005). Introduction to Statistical Thought. Michael Lavine. * Lehmann, E. L., & Casella, G. (2003). Theory of point estimation. Springer. * Bertsekas, D. P., & Tsitsiklis, J. N. (2002). Introduction to Probability. Athena scientific. * Casella, G., & Berger, R. L. (2002). Statistical inference. Cengage Learning. * Shao, J. (2000). Mathematical Statistics. Springer * Schervish, M. J. (1995). Theory of statistics. Springer Science & Business Media. Software See List of Statistical packages for a complete list. * The Lightspeed Matlab Toolbox See also * Statistical Learning Theory * Statistical Signal Processing * Information Theory Other Resources *Video Tutorials - Youtube channel of 'Mathematical Monk' *Probability and Statistics by Khan Academy *Statistics by Wikibooks *Statistics by Wikiversity *Statistics - Notebook *Probability Theory - Notebook *Algorithmic Information Theory - Notebook *Bayesian statistics: a comprehensive course by Ox Educ - Youtube Category:Probability and Statistics